Q1) 10 years ago the average age of all 25 teachers in a school was 45 years. 4 years ago one teacher retired from her post at the age of 58. After one year a new teacher whose age was 54 was recruited from outside. The present average age of all the teachers is ?

A teacher retired at the age of 58 and a year later a teacher joined at the age of 54. The year on which the teacher joined, if that year the first teacher would have retired, then the first teacher's age at that point would have been 59

So there's a net reduction in total of 5This net reduction will be carried forward throughout all the yearsIf nobody would've retired or joined the average of the 25 people would've been 45+10=55, as we are moving 10 years aheadBut remember there's a net reduction of 5 years in totalAs there is no change in the number of teachers, the net reduction in average would be 5/25 = 1/5So the current average should be 55 - 1/5 = 54 4/5

Q2) A, B, C and D purchased a hotel for 56 lakhs. Contribution of B, C and D together is 460% of the contribution of A alone. Contribution of A, C and D is 366.66% that of the B's contribution and contribution of C is 40% of A, B and D together. Contribution of D is ?

Observe few things first: If we have two numbers. Both are increased/decreased by the same value. The difference of the two values should remain constant.

Now, let us apply it here. But before we do that, understand that we can apply it here as both person saves equal amount. And Income - Savings = Expenditure

So, the numerator and the denominator of the first ratio MUST reduce by a constant value to get the second ratio. If that happens the difference between the numerator and denominator must remain constant.

Now, we have the first ratio 7/3 and the second one 5/2In the first ratio, the difference between numerator and denominator is 4 and the in the second one is 3

So multiply both parts in the first ratio by 3, and both parts in the second ratio by 4, to make the difference equal.

we now have 21/9 and 20/8

Now, if we observe the numerator reduce by 1 and so does the denominator. but it should actually reduce by 300. So, we need to multiply by 300, effectively everything here by 300

As, we are looking for the income of the first person, that is 21 parts: it would be 21 * 300 = 6300

If B's age is 10 years more than A's age 5 years back
Then B's age should be 5 years more than A's present age
Now, A's and B's present ages are in the ratio 3:4
and if the gap is 5 years, which corresponds to 1 part in the ratio
B's age must be 20 years, as it is 4 parts in the ratio

First thing that you need to understand is getting the highest power of a certain prime that a given factorial will be divisible by

Let's say what is the maximum power of 2 that will divide 50!

In order to solve that, we will successively divide 50 by 2, and keep collecting the quotients. The answer will be sum of all the quotients

50/2 = 2525/2 = 1212/2 = 66/2 = 33/2 = 1

Thus answer is 25 + 12 + 6 + 3 + 1 = 47

Now, if we need to figure out the max power of a certain composite, we need to check for each prime in the composite ...

In a certain factorial, if we need to check the max power of 2015 = 5 * 13 * 31

we need to check for each primes. But, in any factorial the number of 31s cannot exceed the number of 13s and the number of 5s. Thus, the number 2015s will be determined by 31s. Thus, checking by 31 alone is sufficient

If the question says 2015!!

31! will have one 31, so will 32!, so will 33! ... till 61!So each of these are giving 1 power each, in total 31*1

Q6) The MRP of a chocolate is Rs 65. A customer purchased the chocolate for 56 Rupees 16 Paise. He got two successive discounts of which one is 10%. Find the other discount of the discount scheme that was given by the seller.

Q7) If all the sides of a cuboid increases by 8%, its volume increases by x%
If all the sides of a different cuboid reduces by 8%, its volume reduces by y%
Which of the following is true?
a) x = y
b) x > y
c) x < y
d) We need the initial side ratio of the two cuboids that we begin with

Understand this LOGICALLY
when we have successive change over +a and +a, the net change will be more than 2a
when we have successive change over -a and -a, the net change will be less than 2a
Think over the successive change formula, you'd understand
So, the x% must be greater than y%